In kinematics, if an object moves with constant velocity, what does this imply about both its speed and its direction of motion over time?

Introduction / Context:
In physics, velocity is a vector quantity, meaning it has both magnitude and direction. Speed, on the other hand, is a scalar quantity and only has magnitude. Understanding the difference between these concepts is essential in kinematics and dynamics. When we say an object has constant velocity, we are making a stronger statement than when we say it has constant speed. This question tests whether you can correctly interpret what constant velocity implies about both speed and direction of motion.

Given Data / Assumptions:
• The object is moving and its velocity is described as constant. • Velocity has both magnitude (speed) and direction. • The options separate the ideas of constant speed and constant direction. • We assume uniform motion in a straight line when velocity is constant.

Concept / Approach:
Constant velocity means that the velocity vector does not change with time. A vector can change either by changing its magnitude, by changing its direction, or both. Therefore, if velocity is truly constant, neither its magnitude nor its direction can change. This implies the object moves in a straight line at a uniform speed. If speed changed while direction stayed the same, the magnitude of the velocity vector would change. If direction changed while speed stayed constant, the vector direction would change. In both cases, velocity would not be constant. Hence, constant velocity requires constant speed in a constant direction.

Step-by-Step Solution:
Step 1: Recall that velocity is a vector with magnitude and direction. Step 2: Understand that constant velocity means no change in this vector over time. Step 3: Recognise that a change in speed changes the magnitude of the velocity vector. Step 4: Recognise that a change in direction changes the direction of the velocity vector. Step 5: Conclude that neither magnitude nor direction can change if velocity is constant. Step 6: Therefore, the motion must be at constant speed along a straight line, which is constant direction.

Verification / Alternative check:
You can check this by considering examples. A car moving around a circular track at constant speed does not have constant velocity because its direction changes continuously; it experiences centripetal acceleration. Conversely, a car moving in a straight line but speeding up has changing speed and therefore changing velocity. Only a car moving straight at unchanging speed has constant velocity. Mathematically, constant velocity means that the displacement vector increases linearly with time and the acceleration is zero. These checks confirm that both speed and direction must remain fixed to satisfy constant velocity.

Why Other Options Are Wrong:
Option A suggests constant speed but changing direction, which describes uniform circular motion, not constant velocity. Option B suggests constant direction but changing speed, which corresponds to speeding up or slowing down in a straight line; this also involves non zero acceleration and thus changing velocity. Option D, none of the above, is incorrect because option C is a precise and correct statement of the condition for constant velocity. Therefore, only option C matches the vector definition of constant velocity.

Common Pitfalls:
A common mistake is to treat velocity and speed as if they were the same quantity and assume that constant velocity only means constant speed. Another pitfall is to overlook changes in direction as a form of acceleration, even when speed is unchanged. Remembering that any change in either magnitude or direction of velocity represents acceleration helps clarify why circular motion at constant speed still counts as accelerated motion. Keeping this vector viewpoint in mind will help you correctly interpret many kinematics problems.

Final Answer:
The correct choice is It must have constant speed in a constant direction at all times, because constant velocity requires that neither the magnitude nor the direction of the velocity vector changes with time.